Some digital communication systems use equalization to increase accurate detection of transmitted symbols in the presence of intersymbol interference (ISI). Such systems often use "pulse shaping" so that the resulting pulses have a zero value at the symbol interval (e.g., a Nyquist pulse). Pulse shaping ideally, in the absence of channel distortion, prevents sequences of pulses from interfering with each other when being sampled. For example, the shaping may be configured to achieve Nyquist pulses, which are well known. Channel distortion, for example, due to the receipt of the transmitted signal over multiple paths with different delays, causes ISI even when Nyquist pulses are transmitted. Equalization is required to compensate for this ISI so that the transmitted symbols are accurately detected. Such equalization and pulse shaping systems are well known (see for example, U.S. Pat. Nos. 5,414,734 and 5,513,215 for a discussion of equalization and Proakis, DIGITAL COMMUNICATIONS, third edition, McGraw-Hill, 1995 for a discussion of pulse shaping). FIG. 1 is a simplified diagram illustrative of a system 10 that uses pulse shaping and equalization.
System 10 includes a transmitter 12, a receiver 14 with an equalizer 16. System 10 is a wireless digital system in which transmitter 12 broadcasts radiofrequency (RF) signals that are modulated to include digital information. In this system, transmitter 12 receives symbols x(t), which transmitter 12 modulates and broadcasts. Each symbol generally represents one or more bits. For example, each symbol of a sixteen-level quadrature amplitude modulation (QAM) scheme represents four bits.
Receiver 14 then receives, demodulates, and samples the broadcasted symbols. Although omitted from FIG. 1 for clarity, in system 10 receiver 14 generally receives a transmission through more than one transmission path. For example, the multiple paths may be the result of more than one transmitter being used to transmit the signals and/or the transmitted signal from a single transmitter being reflected from nearby structures. Typically, the transmission paths between receiver 14 and the various other transmitters are not equal in length and may be changing over time (due to the receiver being moved while receiving a symbol), thereby resulting in multipath fading and ISI. Equalizer 16 then compensates for ISI as the ISI changes over time. Receiver 14 then outputs the detected symbols x(t).
Equalizer coefficients can be computed from an estimate of the channel response where the channel is modeled as in model 20 in FIG. 2. Equalization, ISI, and fading are discussed in more detail in the aforementioned U.S. Pat. Nos. 5,414,734 and 5,513,215, which are assigned to the same assignee as the present invention.
FIG. 2 is a diagram illustrative of a simplified model 20 of system 10. In this model, transmitter 12 includes a pulse shaping filter 22. Transmitter 12 generally includes several other components besides pulse shaping filter 22 that can influence the shape of the transmitted waveform, and are omitted from this diagram for clarity. Such effects can be modeled as part of pulse shaping filter 22. Also, receiver 14 generally includes other filters and components that are omitted from the diagram, but can be modeled as part of pulse shaping filter 28. Transmitter 12 receives digital information represented by symbols x(t), applies the pulse shaper, and uses the result to modulate a carrier signal.
Model 20 also includes a physical channel 24, which represents the multiple paths of the fading channel (the additional transmitters are omitted for clarity). In model 20, physical channel 24 is modeled as a filter with a time-variant impulse response. The transmitted signal that is "filtered" by physical channel 24 is then received by receiver 14. A summer 26 is included in model 20 to add noise n(t) to the received signal. Receiver 14 includes a pulse shaping filter 28, which outputs a signal y(t) to equalizer 16. Pulse shaping filters 22 and 28 are configured so that the combined filtering results in a Nyquist pulse when there is no channel distortion or transmitter and receiver effects. In this conventional model, system 10 generates signal y(t) according to definition (1) below: EQU y(t)={[x(t)*p.sub.t (t)*h(t)]+n(t)}*p.sub.r (t) (1)
where y(t), x(t), p.sub.t (t), h(t), and p.sub.r (t), respectively, represent the output signal of pulse shaping filter 28, the symbol to be transmitted, the impulse response of pulse shaping filter 22, the impulse response of physical channel 24, and the impulse response of pulse shaping filter 28 in the time domain. The symbol "*" indicates the convolution operation.
Some conventional systems (e.g., see Crozier, S. N., Falconer, D. D., Mahmoud, S. A., "Least Sum Of Squared Errors (LSSE) Channel Estimation", IEE Proceedings-F, Vol. 138, No. 4, pp. 371-278, August 1991) estimate the overall channel response (i.e., the response due to the pulse shaping filters as well as the physical channel), with symbols x(t) being input into the system. The overall channel is typically modeled as a finite impulse response (FIR) filter, with a predetermined number of coefficients. The number of coefficients is selected to be sufficient to model the channel response without introducing estimation error that significantly affects the performance of the system. In this type of conventional system, the overall channel is modeled according to definition (2) below: EQU G(t,z)=P.sub.t (z)H(t,z)P.sub.r (z) (2)
where G(t,z), P.sub.t (z), H(t,z), and P.sub.r (z), respectively, represent the transfer functions of the overall channel response, the pulse shaping filter 22, the physical channel 24 and the pulse shaping filter 28 in the z domain. It will be appreciated by those skilled in the art that the transfer function of physical channel 24 is time variant and, hence, is denoted as a function of both t and z in definition 2. Thus, the overall channel response is also a function of t and z.
To estimate the time-varying coefficients of the FIR filter implementing G(t,z), a sequence of known pilot symbols is transmitted periodically. Because of the periodic insertion of the sequence of pilot symbols into the stream of data symbols, the transmitted signal has a frame structure. Each frame consists of a sequence of pilot symbols, followed by the data symbols until the start of the next pilot sequence.
To estimate the coefficients of the FIR filter implementing G(t,z) at each frame, the received signal corresponding to the pilot sequence is extracted. The error between the output signal predicted by the model and the observed output signal of the actual system is minimized using iterative or least squares minimization methods to adjust the coefficients of the overall channel FIR filter. For example, the aforementioned paper by Crozier et al. uses a least squares estimation method to determine the coefficients of the overall channel FIR filter.
The number of coefficients used in the overall channel FIR filter model is related to the number of pilot symbols required in the estimation. That is, for a given number of coefficients for the overall channel FIR filter model, there is a minimum required number of pilot symbols in the sequence. Generally, the number of pilot symbols in the sequence must be greater than or equal to the number of FIR filter coefficients. Longer pilot symbol sequences decrease the number of data symbols in a frame, thereby decreasing data throughput.
Generally, for time-invariant systems, the accuracy of the estimation increases as the number of pilot symbols used in the estimation increases. However, in a time-varying system such as system 10 (FIG. 1), the accuracy of the estimation tends to decrease as the number of pilot symbols increases because the increased number of pilot symbols occupies a greater timespan, thereby allowing more time for the channel characteristics to change while being estimated. Thus, in selecting the number of coefficients for the overall channel FIR filter, the designer in effect trades error due to estimation for error due to channel variation. Also, because the estimation is typically performed in software by a processor, the computational load on the processor increases as the number of coefficients increases. Accordingly, there is a need for an equalization system that achieves relatively high accuracy with a reduced number of estimated channel coefficients.